Modifed 1st example to use equations

Previous version used dot(F, x) to compute the prior, which
doesn't look much different from the linear KF.
`
This commit is contained in:
Roger Labbe committed 2018-05-08 15:18:40 -07:00
1 parent be136c1425
commit b5146e3a18
1 file changed
+48 -46
+48 -46
View File
@@ -290,9 +290,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": "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 truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e8aaffd0>"
"<matplotlib.figure.Figure at 0x1d6c66ca7b8>"
]
},
"metadata": {},
@@ -332,9 +332,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9d1fe80>"
"<matplotlib.figure.Figure at 0x1d6c73b0ef0>"
]
},
"metadata": {},
@@ -387,7 +387,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e8aaf828>"
"<matplotlib.figure.Figure at 0x1d6c66ca320>"
]
},
"metadata": {},
@@ -432,14 +432,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Difference in mean x=-0.059, y=44.582\n"
"Difference in mean x=-0.015, y=43.076\n"
]
},
{
"data": {
"image/png": 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truncated
"image/png": "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 truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9d18b00>"
"<matplotlib.figure.Figure at 0x1d6c786aba8>"
]
},
"metadata": {},
@@ -509,7 +509,7 @@
"data": {
"image/png": "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 truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9cec5f8>"
"<matplotlib.figure.Figure at 0x1d6c7814710>"
]
},
"metadata": {},
@@ -539,18 +539,20 @@
"outputs": [],
"source": [
"def fx(x, dt):\n",
" F = np.array([[1., dt], [0, 1]])\n",
" return np.dot(F, x)\n",
" xout = np.empty_like(x)\n",
" xout[0] = x[1] * dt + x[0]\n",
" xout[1] = x[1]\n",
" return xout\n",
"\n",
"def hx(x):\n",
" return x[:1] # return position x "
" return x[:1] # return position [x] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's be clear, this is a linear example. There is no need to use a UKF for a linear problem, but I'm starting with the simplest possible example.\n",
"Let's be clear, this is a linear example. There is no need to use a UKF for a linear problem, but I'm starting with the simplest possible example. But notice how I wrote `fx()` to compute $\\mathbf{\\bar x}$ as a set of equations instead of a matrix multiplication. This is to illustrate that I could implement any arbitrary nonlinear function here; we are not constrained to linear equations.\n",
"\n",
"The rest of the design is the same. Design $\\mathbf P$, $\\mathbf R$, and $\\mathbf Q$. You know how to do that, so let's just finish up the filter and run it."
]
@@ -562,9 +564,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea327b00>"
"<matplotlib.figure.Figure at 0x1d6c7825630>"
]
},
"metadata": {},
@@ -630,7 +632,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea2bb6d8>"
"<matplotlib.figure.Figure at 0x1d6c7e77f28>"
]
},
"metadata": {},
@@ -680,7 +682,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3dadd8>"
"<matplotlib.figure.Figure at 0x1d6c7f1df28>"
]
},
"metadata": {},
@@ -728,7 +730,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3fa6a0>"
"<matplotlib.figure.Figure at 0x1d6c7f66780>"
]
},
"metadata": {},
@@ -785,7 +787,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea327f98>"
"<matplotlib.figure.Figure at 0x1d6c7e1e128>"
]
},
"metadata": {},
@@ -974,7 +976,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9cecef0>"
"<matplotlib.figure.Figure at 0x1d6c7e77940>"
]
},
"metadata": {},
@@ -1093,7 +1095,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea65a828>"
"<matplotlib.figure.Figure at 0x1d6c80ed7f0>"
]
},
"metadata": {},
@@ -1206,7 +1208,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea5ebd68>"
"<matplotlib.figure.Figure at 0x1d6c8153550>"
]
},
"metadata": {},
@@ -1270,7 +1272,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea4d7cf8>"
"<matplotlib.figure.Figure at 0x1d6c80174a8>"
]
},
"metadata": {},
@@ -1444,7 +1446,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea33b978>"
"<matplotlib.figure.Figure at 0x1d6c7e10828>"
]
},
"metadata": {},
@@ -1454,7 +1456,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea60c160>"
"<matplotlib.figure.Figure at 0x1d6c77c3a58>"
]
},
"metadata": {},
@@ -1464,7 +1466,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea4326d8>"
"<matplotlib.figure.Figure at 0x1d6c77bea90>"
]
},
"metadata": {},
@@ -1549,7 +1551,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3c0320>"
"<matplotlib.figure.Figure at 0x1d6c817b470>"
]
},
"metadata": {},
@@ -1649,7 +1651,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3c09b0>"
"<matplotlib.figure.Figure at 0x1d6c7e0f1d0>"
]
},
"metadata": {},
@@ -1714,7 +1716,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3d62e8>"
"<matplotlib.figure.Figure at 0x1d6c811c7b8>"
]
},
"metadata": {},
@@ -1794,7 +1796,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3d62b0>"
"<matplotlib.figure.Figure at 0x1d6c7f28710>"
]
},
"metadata": {},
@@ -1870,7 +1872,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea327780>"
"<matplotlib.figure.Figure at 0x1d6c7e2e940>"
]
},
"metadata": {},
@@ -1977,7 +1979,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea315ac8>"
"<matplotlib.figure.Figure at 0x1d6c7848550>"
]
},
"metadata": {},
@@ -2048,7 +2050,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea619a90>"
"<matplotlib.figure.Figure at 0x1d6c81d66a0>"
]
},
"metadata": {},
@@ -2093,7 +2095,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea6957f0>"
"<matplotlib.figure.Figure at 0x1d6c81ff630>"
]
},
"metadata": {},
@@ -2145,7 +2147,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea2abe80>"
"<matplotlib.figure.Figure at 0x1d6c7ecaa90>"
]
},
"metadata": {},
@@ -2185,7 +2187,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9ce05f8>"
"<matplotlib.figure.Figure at 0x1d6c7f8f710>"
]
},
"metadata": {},
@@ -2589,7 +2591,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea315630>"
"<matplotlib.figure.Figure at 0x1d6c7e72cf8>"
]
},
"metadata": {},
@@ -2599,7 +2601,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea53d588>"
"<matplotlib.figure.Figure at 0x1d6c7fae198>"
]
},
"metadata": {},
@@ -2609,7 +2611,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea2d7160>"
"<matplotlib.figure.Figure at 0x1d6c813bb00>"
]
},
"metadata": {},
@@ -2688,7 +2690,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea51bb00>"
"<matplotlib.figure.Figure at 0x1d6c81b9550>"
]
},
"metadata": {},
@@ -2698,7 +2700,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8e9d9e518>"
"<matplotlib.figure.Figure at 0x1d6c7faa940>"
]
},
"metadata": {},
@@ -2708,7 +2710,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea3a8f98>"
"<matplotlib.figure.Figure at 0x1d6c82723c8>"
]
},
"metadata": {},
@@ -2895,7 +2897,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea51bcc0>"
"<matplotlib.figure.Figure at 0x1d6c7f220b8>"
]
},
"metadata": {},
@@ -3312,7 +3314,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea75fda0>"
"<matplotlib.figure.Figure at 0x1d6c7842e80>"
]
},
"metadata": {},
@@ -3399,7 +3401,7 @@
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea739940>"
"<matplotlib.figure.Figure at 0x1d6c831be10>"
]
},
"metadata": {},
@@ -3439,7 +3441,7 @@
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1b8ea51bf60>"
"<matplotlib.figure.Figure at 0x1d6c82a98d0>"
]
},
"metadata": {},